China Ocean Engineering

, Volume 28, Issue 6, pp 791–806 | Cite as

Comparative study of different SPH schemes on simulating violent water wave impact flows

  • Xing Zheng (郑 兴)
  • Qing-wei Ma (马庆位)
  • Wen-yang Duan (段文洋)


Free surface flows are of significant interest in Computational Fluid Dynamics (CFD). However, violent water wave impact simulation especially when free surface breaks or impacts on solid wall can be a big challenge for many CFD techniques. Smoothed Particle Hydrodynamics (SPH) has been reported as a robust and reliable method for simulating violent free surface flows. Weakly compressible SPH (WCSPH) uses an equation of state with a large sound speed, and the results of the WCSPH can induce a noisy pressure field and spurious oscillation of pressure in time history for wave impact problem simulation. As a remedy, the truly incompressible SPH (ISPH) technique was introduced, which uses a pressure Poisson equation to calculate the pressure. Although the pressure distribution in the whole field obtained by ISPH is smooth, the stability of the techniques is still an open discussion. In this paper, a new free surface identification scheme and solid boundary handling method are introduced to improve the accuracy of ISPH. This modified ISPH is used to study dam breaking flow and violent tank sloshing flows. On the comparative study of WCSPH and ISPH, the accuracy and efficiency are assessed and the results are compared with the experimental data.

Key words

smoothed particle hydrodynamics (SPH) ISPH water wave impact 


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  1. Cleary, P. W. and Monaghan, J. J., 1999. Conduction modeling using smoothed particle hydrodynamics, J. Comput. Phys., 148(1): 227–264.CrossRefMathSciNetMATHGoogle Scholar
  2. Colagrossi, A. and Landrini, M., 2003. Numerical simulation of interfacial flow by smoothed particle hydrodynamics, J. Comput. Phys., 191(2): 448–475.CrossRefMATHGoogle Scholar
  3. Cummins, S. J. and Rudman, M., 1999. An SPH projection method, J. Comput. Phys., 152(2): 584–607.CrossRefMathSciNetMATHGoogle Scholar
  4. Gao, R., Ren, B., Wang, G. Y. and Wang, Y. X., 2012. Numerical modeling of regular wave slamming on surface of open-piled structures with the corrected SPH method, Appl. Ocean Res., 34, 173–186.CrossRefGoogle Scholar
  5. Gingold, R. A. and Monaghan, J. J., 1977. Smoothed particle hydrodynamics: Theory and application to non-spherical stars, Mon. Not. R. Astron. Soc., 181(3): 375–389.CrossRefMATHGoogle Scholar
  6. Hirt, C. W. and Nichols, B. D., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comput. Phys., 39(1): 201–225.CrossRefMATHGoogle Scholar
  7. Hu, X. Y. and Adams, N. A., 2007. An incompressible multi-phase SPH method, J. Comput. Phys., 227(1): 264–278.CrossRefMATHGoogle Scholar
  8. Faltinsen, O. M., 1978. A numerical nonlinear method of sloshing in tanks with two dimensional flow, J. Ship Res., 22(3): 193–202.Google Scholar
  9. Kishev, Z. R., Hu, C. H. and Kashiwagi, M., 2006. Numerical simulation of violent sloshing by a CIP-based method, J. Mar. Sci. Technol., 11(2): 111–122.CrossRefGoogle Scholar
  10. Koshizuka, S. and Oka, Y., 1996. Moving particle semi-implicit method for fragmentation of incompressible fluid, Nucl. Sci. Eng., 123(3): 421–434.Google Scholar
  11. Liang, D. F., Thusyanthan, N. M., Madabhushi, S. P. G. and Tang, H. W., 2010. Modelling solitary waves and its impact on coastal houses with SPH method, China Ocean Eng., 24(2): 353–368Google Scholar
  12. Lee, E. S., Moulinec, C., Xu, R., Violeau, D., Laurence, D. and Stansby, P., 2008. Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method, J. Comput. Phys., 227(18): 8417–8436.CrossRefMathSciNetMATHGoogle Scholar
  13. Liu, G. R. and Liu, M. B., 2003. Smoothed Particle Hydrodynamics—A Meshfree Particle Method, World Scientific Press.CrossRefMATHGoogle Scholar
  14. Liu, M. B., Liu, G. R., Lam, K. Y. and Zong, Z., 2003. Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Comput. Mech., 30(2): 106–118.CrossRefMATHGoogle Scholar
  15. Lo Edmond, Y. M. and Shao, S. D., 2002. Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Appl. Ocean Res., 24(5): 275–286.CrossRefGoogle Scholar
  16. Lucy, L. B., 1977. A numerical approach to the testing of the fusion process. Astron. J., 82, 1013–1024.CrossRefGoogle Scholar
  17. Ma, Q. W., 2008. A new meshless interpolation scheme for MLPG_R method, Computer Modeling in Engineering & Sciences, 23(2): 75–89.MathSciNetMATHGoogle Scholar
  18. Ma, Q. W. and Zhou, J. T., 2009. MLPG_R method for numerical simulation of 2D breaking waves, Computer Modeling in Engineering & Sciences, 43(3): 277–304.MathSciNetMATHGoogle Scholar
  19. Marrone, S., Antuono, M., Colagrossi, A., Colicchio, G., Le Touze, D. and Graziani, G., 2011. δ-SPH model for simulating violent impact flows, Comput. Method. Appl. Mech. Eng., 200, 1526–1542.CrossRefMATHGoogle Scholar
  20. Martin, J. C. and Moyce, W. J., 1952. Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane, Phil. Trans. R. Soc. Lond. A., 244(882): 312–324.CrossRefMathSciNetGoogle Scholar
  21. Monaghan, J. J., 1994. Simulation free surface flows with SPH, J. Comput. Phys., 110(2): 399–406.CrossRefMATHGoogle Scholar
  22. Monaghan, J. J., 1997. SPH and Riemann solvers, J. Comput. Phys., 136(2): 298–307.CrossRefMathSciNetMATHGoogle Scholar
  23. Pan, C. H., Xu, X. Z. and Lin, B. Y., 1993. Simulating free surface flows by MAC method, Estuary Coastal Engineering, (1–2): 51–58. (in Chinese)Google Scholar
  24. Pan, X. J., Zhang, H. X. and Sun, X. Y., 2012. Numerical simulation of sloshing with large deforming free surface by MPS-LES method, China Ocean Eng., 26(4): 653–688.CrossRefGoogle Scholar
  25. Pan, X. J., Zhang, H. X. and Lu, Y. T., 2008. Moving-particle semi-implicit method for vortex patterns and rolls damping of 2D ship sections, China Ocean Eng., 22(3): 399–407.Google Scholar
  26. Parshikov, A. N. and Medin, S. A., 2002. Smoothed particle hydrodynamics using interparticle contact algorithms, J. Comput. Phys., 180(1): 358–382.CrossRefMATHGoogle Scholar
  27. Rafiee, A., Cummins, S., Rudman, M. and Thiagarajan, K., 2012. Comparative study on the accuracy and stability of SPH schemes in simulating energetic free-surface flows, Eur. J. Mech., B/Fluids, 36, 1–16.CrossRefMathSciNetMATHGoogle Scholar
  28. Shao, S. D. and Lo Edmond, Y. M., 2003. Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Adv. Water Resour., 26(7): 787–800.CrossRefGoogle Scholar
  29. Shao, S. D., Ji, C. M., Graham, D. I., Reeve, D. E., James, P. W. and Chadwick, A. J., 2006. Simulation of wave overtopping by an incompressible SPH model, Coast. Eng., 53(9): 723–735.CrossRefGoogle Scholar
  30. Shao, S. D., 2009. Incompressible SPH simulation of water entry of a free-falling object, Int. J. Numer. Methods Fluids, 59(1): 91–115.CrossRefMATHGoogle Scholar
  31. Zhang, A. M., Yang, W. S. and Yao, X. L., 2012. Numerical simulation of underwater contact explosion, Appl. Ocean Res., 34, 10–20.CrossRefGoogle Scholar
  32. Zheng, X., Duan, W. Y. and Ma, Q. W., 2012a. A new scheme for identifying free surface particles in improved SPH, Sci. China, Ser. G, 55(8): 1454–1463.CrossRefGoogle Scholar
  33. Zheng, X., Ma, Q. W. and Duan, W. Y., 2012b. Simulation of breaking waves by using an improved SPH, Proc. 22nd Int. Offshore Polar Eng. Conf., Rhodes, Greece, 3, 1051–1056.Google Scholar
  34. Zhou, J. T., Ma, Q. W. and Yan, S., 2008. Numerical implementation of solid boundary condition in meshless methods, Proc. 18th Int. Offshore Polar Eng. Conf., Vancouver, Canada, 3, 16–23.Google Scholar

Copyright information

© Chinese Ocean Engineering Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Xing Zheng (郑 兴)
    • 1
  • Qing-wei Ma (马庆位)
    • 1
    • 2
  • Wen-yang Duan (段文洋)
    • 1
  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina
  2. 2.Schools of Engineering and Mathematical ScienceCity UniversityLondonUK

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